Put the egg yolks into a blender or bowl and whisk or blend until smooth. Add the garlic, lemon juice and mustard and blend again until mixed.
Working very, very slowly, add the oil while blending or whisking at a low speed, starting with the olive oil, then the coconut oil. Start with a drop at a time until it starts to emulsify, then keep adding the oil slowly until all the oil has been incorporated.
Stir in the chopped chives. Stored in an airtight container or screw-top jar, this dressing will keep in the fridge up to one week.